Monday, July 29, 2013

I think I have a bit more to say about boundaries, especially in terms of the boundaries that distinguish the academic disciplines. I've been arguing that the boundaries between, say, history and physics are nowhere near as rigid and as static as academic purists might insist, but neither are the boundaries between history and physics imaginary, capricious, and unnecessary as academic anarchists might insist. (I recognize that I am creating extremes with my contrast of purists and anarchists and that most educationists lie somewhere between or even outside these two extremes, but it helps me to see my point.) Boundaries are both necessary for human activity and knowledge and temporary.

I rely here on a few articles by South African complexity scholar Paul Cilliers and by Dave Snowden's Cynefin Framework, and my argument, I think, makes a basic assumption: that education and educational structures are complex systems tending to the chaotic, rather than complicated systems tending to the simple. I believe this is so despite the enormous energy expended in wrenching education into a simple system. Education ain't simple. It probably isn't even complicated. It's complex, at best. To my mind, then, the biggest problem with academic disciplines is that we try to move them into the simple and/or complicated domains of the Cynefin Framework where their boundaries are fixed, explicit, and easily taught, with clear canons of content and methodologies. In the simple or even complicated domains, it's easy to distinguish the historian from the physicist. In the complex domain, disciplinary and canonical boundaries are much more problematic, though no less useful, even necessary. Paul Cilliers helps me understand this.

In several critiques (Knowledge, Complexity, and Understanding (2000), Knowledge, limits and boundaries (2005), and Why We Cannot Know Complex Things Completely (2007), for instance), Cilliers argues that knowledge is best understood as an emergent property "constituted within a complex system of interactions". This view of knowledge avoids both extremes of the purist and the anarchist, or as Cilliers more accurately calls them: the fundamentalist and the relativist. As Cilliers says:

An understanding of knowledge as constituted within a complex system of interactions would, on the one hand, deny that knowledge can be seen as atomised ‘facts’ that have objective meaning. Knowledge comes to be in a dynamic network of interactions, a network that does not have distinctive borders. On the other hand, this perspective would also deny that knowledge is something purely subjective, mainly because one cannot conceive of the subject as something prior to the ‘network of knowledge’, but rather as something constituted within that network. The argument from complexity thus wants to move beyond the objective/subjective dichotomy. (Knowledge, limits and boundaries, p. 608)

Knowledge, then, is not representational, "linked to the sign which represents it", but relational, "the result of a dynamic interaction between all the meaningful components in the system … itself a complex process" (Why We Cannot Know Complex Things Completely, p. 85). This presents an immediate problem, however, given the open nature of complex systems. If complete knowledge must account for an infinite number of interactions across the open boundaries of complex systems, then how do we ever attain actionable knowledge, given that we have a limited amount of time? Because we, as knowledge makers, are ourselves contextualized, and each context limits the number of system components presented for knowledge making. In other words, though a single rose is ultimately connected through its complex interactions to the entire rest of the Universe, the meaning of the rose is constrained when I cut it from my own garden and present it to my wife on Valentine's Day, which provides a bounded context within which meaning can emerge. The boundaries make the emergence of a particular meaning possible.

Of course, the meaning is no more absolute than the boundaries that enable it. In the relatively straightforward example above, the meaning of the rose will be slightly different, perhaps radically different, for me than for my wife as we bring our different contexts to the event, but it will be similar enough that we can at least speak meaningfully with each other—though we should be mindful that the very stuff of most romantic comedies involves the different meanings drawn by men and women from even so well-bounded and commonly shared an event as Valentine's Day. Boundaries in complex systems are not permanent or rigid, though they can persist in recognizable contours for long times.

So to directly address my concerns with Marion Brady's dismissal of disciplinary boundaries, I think he slightly overstates his case. We cannot dispense with boundaries in complex systems such as academic disciplines if we want to create meaning, or knowledge. Likewise, we cannot calcify our boundaries without destroying knowledge. As Cilliers says it:

One can, and often should, emphasise the interrelatedness of systems. Often the boundaries of systems are constructions we impose in order to reduce the complexity. This can lead to oversimplifications, to reductive descriptions of the system. However, if boundaries become too vague, we end up with a kind of holism which does not allow much to be said. … We need limits in order to say something. (Why We Cannot Know Complex Things Completely, p. 88)

Perhaps, though, Brady's discontent with disciplinary boundaries comes from the usual interpretation of boundaries as "something that separates one thing from another" (Knowledge, limits and boundaries, p. 611). In this view of boundaries, one cannot be both an historian and a physicist at the same time. History and physics are separate things, and one cannot be in both places at once. Of course, complexity and quantum theories ignore this kind of classical logic. Cilliers makes some suggestions about how we might think differently about boundaries, ways that make sense within complex systems.

First, "we should rather think of a boundary as something that constitutes that which is bounded. This shift will help us to see the boundary as something enabling, rather than as confining" (p. 611). From this view, our skins, those well-known and most familiar boundaries, don't separate us from the rest of the world; rather, they enable our interaction with the world by helping to maintain our own integrity as a persisting complex system and providing somewhat stable and recognizable contours that the rest of the world can engage and through which energy and information may be exchanged. Likewise, disciplinary boundaries need not separate historians from physicists, but they should enable useful, valuable interaction between historians and physicists, shifting and stretching as different issues supply different contexts of meaning, again enabling a mutually valuable exchange of energy and information.

Next, we should rethink our physical images about the place of a boundary. We must replace our visual metaphors which force us to think of complex systems "as something contiguous in space." Complex social systems, Cilliers notes, are not necessarily contiguous; thus, "parts of the system may exist in totally different spatial locations." This is certainly the case with history as an academic discipline, which is not a spatially contiguous physical system. This implies that a historian likely belongs to many different complex systems (families, churches, political parties, etc) and "that different systems interpenetrate each other, that they share internal organs." So where's the boundary? It's always provisional, determined by the context referenced at any given time for any given event. Furthermore, Cilliers notes that any node in a system is "never far away from the boundary. If the components of the system are richly interconnected, there will always be a short route from any component to the 'outside' of the system. … the boundary is folded in, or perhaps, the system consists of boundaries only. Everything is always interacting and interfacing with others and with the environment; the notions of 'inside' and 'outside' are never simple and uncontested" (p. 611).

So maybe that can address Brady's concerns with disciplinary boundaries. At least somewhat.

Saturday, July 20, 2013

In my last post, I quoted Marion Brady's observations about the transdisciplinary nature of thought and learning, what he calls Theory R: "Theory R requires students to make connections, to perceive relationships, and to synthesize ideas. It sends students searching the far corners of their minds without regard for the artificial, arbitrary boundaries imposed by academic disciplines." I think I understand Brady's point about and his disdain for the "artificial, arbitrary boundaries imposed by academic disciplines." I am entranced with transdisciplinarity and agree with the need to transcend boundaries that are too often impediments to learning and research, but I think Brady overstates the case, ignoring the necessity of boundaries for knowledge and action.

I recently came across Kurt A. Richardson's 2001 article On the Status of Natural Boundaries: A Complex Systems Perspective which helps me clarify my thinking on this issue. Richardson uses complexity theory to guide him through the dilemma of reductionism on one hand, in which boundaries are clear, discrete, and persistent, and holism on the other hand, in which boundaries disappear altogether as everything merges into the Universe or God.

Richardson begins by making a very useful distinction between complex and complicated systems. He states that he is concerned with complex systems, which he defines neatly:

A complex system is comprised of a large number of non-linearly interacting non-decomposable elements. The interactivity must be such that the system cannot be reducible to two or more distinct systems, and must be sufficient (where the determination of sufficient is problematic) to allow the system to display the behaviours characteristic of such systems. (p. 230)

He then clarifies the difference between these complex systems and the often similar looking complicated systems:

The principle difference between a complicated system and a complex system is not the presence of large numbers of entities and nonlinear interactions. The key difference is the nature of the overall connectivity, particularly the existence of feedback mechanisms. Despite the existence [of] nonlinearity complicated systems do not self-organise into new structures. They do not display a wide range of qualitatively different behaviours. The extent and nature of the nonlinear interactivity is what differentiates between a complicated and complex system. The division between these two categories at a compositional level is very blurred however. It is problematic to know from compositional information whether a system is complicated or complex without having information about its behaviour. Complicated and complex systems, then, can only safely be differentiated from each other by observing their respective behaviours.

A complicated system, then, is like a modern jet fighter: large numbers of entities with a myriad of interactions, including some nonlinear interactions, among its parts; however, the jet fighter is incapable of evolving, or self-organizing into new structures.

This distinction between complicated and complex systems helps me to understand the traditional classroom and the value of cMOOCs. A traditional school is a complicated system composed of large numbers of entities and interactions. Some classes are complicated systems, say those with students exceeding Dunbar's Number, but most are simple systems composed of a fixed number of entities (1 teacher and 25 students) and a few, mostly linear interactions: curriculum + instruction —> student learning. In such simple/complicated systems, boundaries are fixed, clear, and enforced. The subsystems (teacher, students, curriculum, lessons, texts, etc) are rigidly differentiated and the interactions among them are stable, predictable, and enforceable. The boundaries are in place and real, and any blurring of a boundary is considered a failure by purists or as a daring experiment in free learning by rebels. Either way, the reality of the boundary is reinforced. Violating a boundary confirms the boundary just as much as enforcing the boundary.

cMOOCs, unlike traditional classrooms and xMOOCs, are intentionally complex systems. cMOOCs and xMOOCs are differentiated by their respective behaviors. Like xMOOCs and some traditional classes, cMOOCs have large numbers of entities with a myriad of interactions, but unlike those complicated systems, cMOOCs can and do self-organize into different and new structures. They evolve through nonlinear interactions, feedback loops, non-local causalities, dialogic tensions, and a range of other behaviors characteristic of complex systems, and new structures of people and ideas emerge that could not have been anticipated by the designers of the MOOC. These complex interactions unfold across blog posts, tweets, Youtube videos, Flickr posts, and coffee cups, and new patterns of people and ideas emerge out of the interactions. Boundaries in cMOOCs, as in other complex systems, are different than the boundaries in simple and complicated systems.

Complex systems, then, are difficult to evaluate. Simple/complicated systems, with their fixed entities and interactions, have a strict linear progression which leads to a predictable, and usually measurable, outcome (if a teacher does A + B + C, then the student must learn D, which we can measure on a test and repeat A + B + C until the student learns D). However, as Richardson points out, complex systems "display many possible qualitatively different behavioural regimes (the nature and variety of which evolve), as well as exhibiting emergence, i.e. the emergence of macroscopic system structures and behaviours that are not at all obvious from their microscopic make-up … The order parameters that best describe the current behaviour of a complex system are not fixed, they evolve qualitatively as well as quantitatively." Factor in the butterfly effect (systemic sensitivity to initial conditions), and it's easy to see how difficult it becomes to predict the outcomes of any given cMOOC. This inability to predict outcomes changes the nature of evaluation. If we do not have a fixed, predictable outcome, then how do we measure the efficacy of the instruction?

Well, I seem to be slipping away from my original point about boundaries, but only a bit. A fixed, predictable outcome is a kind of boundary. It is an endpoint, a destination. In a traditional class or xMOOC, that boundary is discrete. A cMOOC does not have an endpoint or destination. Rather, it is more like another complex system, thunderstorms. Like thunderstorms, cMOOCs build in intensity, form their new structures (not random, but not totally predictable either), expend their energy, and subside, though they can continue to echo long after the thunder has stopped. So here's Richardson's main point about the distinction between complicated and complex systems: "the boundaries describing subsystems in a complicated system are prescribed and fixed whereas the boundaries delimiting subsystems in a complex system are emergent and temporary."

Anyone who has been in a cMOOC can see this fluidity of boundary, for instance, in deciding who is a student in the MOOC and who isn't. If you define student as someone who is actively participating in the MOOC, then that shifts wildly from week to week as people engage, disengage, get distracted, re-engage. And who's the teacher? That can be slippery as well. You can easily measure and quantify enrollment in a traditional class. Measuring a cMOOC is more like measuring a thunderstorm. Just when is a cloud part of the thunderstorm, and when isn't it? That can be hard to quantify or even qualify. The boundary keeps shifting as the thunderstorm, or cMOOC, evolves in its phase space. Come to think of it, developing procedures for defining the phase space of a cMOOC might be a fine start to evaluating them, but it's beyond my abilities.

So what does Richardson say about boundaries in complex systems? In short: "The only real absolute boundaries in a complex system are those that define the basic constituents and their interrelationships. All other boundaries are emergent and temporary. In order to relate these arguments to the real world it is assumed in addition that the universe is a complex system, i.e. the one and only well-defined system." He's having his cake and eating it, too, which is entirely permissible. The only complex system with absolute boundaries is the Universe itself. All other boundaries—in other words, everything else that we know about, including superstrings—are emergent and temporary. Now, curiously enough, this includes both traditional classrooms and xMOOCs as well as cMOOCs; the difference is that cMOOCs recognize and encourage emergent and temporary boundaries and structures, while xMOOCs and traditional classrooms pretend that their boundaries and structures are permanent and in some way blessed or sanctioned.

Okay, then, let's assume for the sake of argument that boundaries really are emergent and temporary. Does that mean that anything goes, that we can create boundaries where we wish as we wish, as the constructivists would have?

Richardson says no. He insists that we do not need to resort either to a constructivism that insists that "all boundaries are created in our minds and as such do not correlate with objective reality at all" or to a naive realism that insists that our ideas "perfectly map to their espoused objects." We can map reality, and those maps are based on the interactions of two complex systems, which implies a complex interaction: natural reality and conceptual reality. As Richardson says of the relationship between the natural and conceptual:

Rather than having a fixed relationship with natural boundaries, or having no relationship at all, conceptual boundaries do have a complex and changing relationship to reality. Sometimes this link might be so tenuous as to be unusable. Sometimes this link is so strong as to give us the impression that we might actually have absolute Truth to hand.

As Richardson says, "In the field of complexity there is evidence that, though there may be no real boundaries, there are resilient and relatively stable emergent structures." Mapping the world, then in the sense of Deleuze and Guattari's cartography, is problematic, but it is not impossible. Boundaries both conceptual and natural make that mapping possible, even necessary. They also make it temporary and emergent.

Thursday, July 18, 2013

In his 2004 Phi Beta Kappan essay entitled Thinking Big: A Conceptual Framework for the Study of Everything, self-described contrarian educator Marion Brady writes that "the main task of educating is to help students make more sense of the world, themselves, and others" (p. 277). He attacks the current state of knowledge as represented in the plethora of academic subjects and disciplines and insists that such a fragmented approach to knowledge will, in the words of Buckminster Fuller, "be the undoing of the society." He quotes Fuller again in a marvelous 1980s complaint to American educators: "What you fellows in the universities do is make all the bright students into experts in something. That has some usefulness, but the trouble is it leaves the ones with mediocre minds and the dunderheads to become generalists who must serve as college presidents . . . and presidents of the United States." I truly wish I had said that, but … well, he was Buckminster Fuller.

Brady then identifies the basic theory of education that underlies the fragmented, disciplinary approach to knowledge:

The present curriculum, made up as it is of separate, specialized studies, exerts considerable pressure on teachers to make major use of what could be called “Theory T.” Theory T dominates American education. … T stands for “transfer.” Those who accept Theory T believe that knowledge is located in teachers’ heads, textbooks, reference materials, and on the Internet and that the instructional challenge is to transfer it from these locations into the empty space in students’ heads. The degree of success of the transfer process can be measured with relative ease, which helps explain its broad appeal. … Evaluating performance is simple enough to allow student responses to be scored by a machine. (pp. 279, 280)

He then contrasts Theory T with what he calls Theory R:

Theory R assumes not that students’ heads are empty but that they are full. The primary instructional challenge, then, is not to transfer new knowledge but to help students reorganize existing knowledge to make it more useful, consistent, or true and to supplement it with insights and skills that will help explain more fully what they already know.… Students in Theory R classrooms must be active processors of information. Theory T emphasizes recall; Theory R requires students to engage in every known thought process. … Theory R requires students to make connections, to perceive relationships, and to synthesize ideas. It sends students searching the far corners of their minds without regard for the artificial, arbitrary boundaries imposed by academic disciplines.

Brady gives here a neat precursor to Connectivism, I think. First, he emphasizes that each student already possesses all the neuronal networks needed for making connections, perceiving relationships, and synthesizing ideas. We teachers do not transfer anything into the imagined empty memory slots of student brains; rather, we present them with a, hopefully, coherent and engaging series of artifacts and experiences to which they may connect, perceive relationships, and synthesize ideas, or not. All too often what they connect to, perceive relationships among, and synthesize are ideas that we never taught, or didn't know we were teaching. And each student makes these connections and patterns within an ecosystem (their own life stories) that we teachers know little to nothing about, and that ecosystem, that context, provides almost all of the meaning for whatever new connections and patterns the student is weaving. This reminds me much of Paul Cilliers' definition of knowledge as "information that is situated historically and contextually by a knowing subject" (Why We Cannot Know Complex Things Completely in Capra, Juarrero, Sotolongo, and van Uden's Reframing Complexity: Perspectives from North and South, 2007, p. 85). In other words, while information may exist apart from our students as data, it does not become knowledge until the student situates that information within a context that includes themselves and that necessarily informs the information in ways we teachers cannot predict or control.

But what most impressed me about Brady's article was his observation that this process of making connections (mapping, as Deleuze and Guattari say) "sends students searching the far corners of their minds without regard for the artificial, arbitrary boundaries imposed by academic disciplines." It seems to me that Connectivism and MOOCs are wonderful vehicles for transdisciplinarity, which transcends the "boundaries imposed by academic disciplines." I know that the MOOCs I have joined have had a marvelous, transdisciplinary reach in content and participants. Though I have had some of the most engaging and rewarding conversations of my professional life, as far as I know, I have actually had no conversation with another writing teacher, aside from one colleague who shared an office with me and a few MOOCs. Almost all of my conversations have been with scholars and practitioners outside my discipline, which makes my engagement in the MOOCs most transdisciplinary.